There are three problems in designing an imaging spectrometer where light in a slice of an image field passing through an entrance slit is to be diffracted by a grating parallel to the slit and imaged onto a focal plane for display or recording with good spatial resolution parallel to the slit and good spectral resolution perpendicular to the slit:
1. Eliminating astigmatism over the spectrum on the image plane. PA1 2. Removing field curvature from the spectrum focused onto the image plane. PA1 3. Obtaining good spatial resolution of the entrance slit which involves eliminating astigmatism at different field angles from points on the entrance slit.
The third problem is probably the most difficult to accomplish. In conventional imaging spectrometers, the spectrometer size is increased until the astigmatism at different field angles is reduced to an acceptable level. This technique is effective because increasing the spectrometer size for a given slit size reduces the field angle through the spectrometer, leading to a reduction of field aberrations such as astigmatism. But for some applications, such as for aerospace instrumentation, a small design volume is important.
Development of a diffraction grating spectrometer based on an Offner 1:1 imaging system for off-axis objects is reported by Deborah Kwo, George Lawrence and Michael Chrisp, "Design of a grating spectrometer from a 1:1 Offner mirror system," SPIE, 818, 275-9 (1987). That grating spectrometer was composed of a large concave spherical mirror facing a concentric convex secondary mirror, both having their center of curvature at the same point on a plane that contains the object (slit) on one side of the convex secondary mirror and an image detector array on a side of the convex secondary mirror opposite the object. The convex secondary mirror was modified by placing a diffraction grating on it with straight grooves perpendicular to the plane of symmetry and parallel to the entrance slit.
With that prior-art design of a reflection grating imaging spectrometer, all third order aberrations were zero leaving only fifth order astigmatism. That astigmatism required slight adjustment of the grating configuration (facilitated by using holographic techniques to produce the grating) and a slight tilt of the convex grating as additional control parameters. However, any tilt of the convex grating destroys the symmetry of the system and introduces coma in the image. Furthermore, only a grating of less than 25 l/mm is possible, thus limiting the upper end of the spectral range.